The insulins listed above need no prescription to be purchased in the US. Rule of thumb is that if it is an analog insulin, it will require a prescription. The beef and pork insulins of CP Pharma require Rx because they are not US-FDA-approved, and the veterinary insulins available in the US (Vetsulin, ProZinc), were FDA-approved as prescription-only medications. Though not required by law, the policy of the pharmacy you deal with may be to require a prescription.

In the US, whether or not you need a prescription for syringes/pen needles is determined by state, not US, law. The laws of your state [3] will apply re: syringes/pen needles requiring a prescription. If you order syringes or pen needles online, the law of the state where you're ordering them from will apply. If you order from a business whose state does not require a prescription for syringes or pen needles, you will not need one, even if the laws of your state of residence say you do. Conversely, if you live in a state where there's no mandatory prescription for syringes or pen needles and order from a company in a state where a prescription is necessary, you will need one to do business with them.

The difference here, for those in the US regarding insulins and syringes is that federal law (US-FDA) regulates which insulins are prescription required, but state law governs whether one is needed for syringes and pen needles.

Even if you buy syringes and pen needles from a local pharmacy and don't live in a state which requires a prescription for them, the policy of the pharmacy itself may be to require a prescription for them.